Question

The Delaware River Joint Toll Bridge Commission increased the tool on the bridges on Route 22 and Interstate 78 from New Jersey to Pennsylvania from $0.50 to $0.75 in December. In November, the Route 22 bridge had 519,337 crossings and the Interstate 78 bridge had 728,002. Suppose that the price elasticity of demand for the Route 22 bridge was .2696 and that for the Interstate 78 bridge was 1.556. (Assume nothing other than the toll change occurred during the months that would affect consumer demand.)

a) How did the revenue from the two bridges change in December? (Be specific.)

b) Suppose that the Commission wanted to increase total revenue from each bridge and could set different prices for the two bridges. Should they be the same or different? If they are the same, should they increase? If they are different, how should they change the prices? (You don’t need to provide a specific price, but just the direction.)

Answer 1

a) Price increased from $0.5 to $0.75

%change in price = [(0.75 - 0.50) / 0.50] * 100 = 50%

Crossings on 22 bridge = 519,337

Crossings on 78 bridge = 728,002

Elasticity of demand for 22 bridge = 0.2696

Elasticity of demand for 78 bridge = 1.556

Elasticity of demand is calculated as %change in quantity demanded / %change in price

For 22 bridge: 0.2696 = %change in quantity demanded / 50%

%change in quantity demanded = 13.48%

Thus crossing of 22 bridge fall from 519,337 to 449,330

Initial revenue of 78 bridge = 0.5 * 519,337 = 259,668.5

New revenue for 78 bridge = 0.75 * 449,330 =  336,997.5

For 78 bridge: 1.556 = %change in quantity demanded / 50%

%change in quantity demanded = 77.8%

Thus crossing of 22 bridge fall from 728,002 to 161,616

Initial revenue of 78 bridge = 0.5 * 728,002 = 364,001

New revenue for 78 bridge = 0.75 * 161,161 =  121,212

We can see that rise in price reduce total revenue of elastic market and raise revenue of inelastic market.

b) If they wanted to increase total revenue, they should set high price for 22 bridge and low for 78 bridge because consumers cannot reduce their demand in inelastic market.